Question

Consider a three-factor APT model. The factors and associated risk premiums are: Risk Premium (%) Factor Change in gross national product (GNP) Change in energy prices Change in long-term interest rates +6.4 0.6 +2.8 Calculate expected rates of return on the following stocks. The risk-free interest rate is 6.5% a. A stock whose return is uncorrelated with all three factors. (Enter your answer as a percent rounded to 1 decimal place.) b. A stock with average exposure to each factor (i.e., with b 1 for each). (Enter your answer as a percent rounded to 1 decimal place.) c. A pure-play energy stock with high exposure to the energy factor (b 2.5) but zero exposure to the other two factors. (Enter your answer as a percent rounded to 2 decimal places.) d. An aluminum company stock with average sensitivity to changes in interest rates and GNP, but negative exposure of b-1.6 to the energy factor. (The aluminum company is energy-intensive and suffers when energy prices rise.) (Enter your answer as a percent rounded to 2 decimal places.) Expected rate of return а. % b. Expected rate of return Expected rate of return Expected rate of return % C. d.

Answer 1

Expected rate of return = Risk free rate + beta * risk premium

a.

Stocks return is correlated with risk factors, this means beta of stock is zero (0).

therefore

Expected rate of return = Risk free rate = 6.5%

b.

Beta = 1

Risk premium = 6.4% + .6% + 2.8% = 9.8%

Expected rate of return = 6.5% + 1*9.8% = 6.5% + 9.8% = 16.3%

c.

Beta = 2.5

Risk Premium = change in energy prices = .6

Expected rate of return = 6.5% + 2.5*.6% = 6.5% + 1.5% = 8%

d.

Beta for GNP and interest rates = 1

GNP and Interest rate risk premium = 6.4% + 2.8% = 9.2%

Beta for energy prices = -1.6

energy prices risk premium = .6

Expected rate of return = 6.5% + 1*9.2% - (1.6 * .6)= 6.5% + 9.2% - 0.96%= 14.74%

Summary

a. Expected rate of return = 6.5%

b. Expected rate of return = 16.3%

c. Expected rate of return = 8%

d. Expected rate of return = 14.74%